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In an examination, the average marks obtained by students who passed was $x\%$, while the average of those who failed was $y\%$. The average marks of all students taking the exam was $z\%$. Find in terms of $x, y$ and $z$, the percentage of students taking the exam who failed.

1. $\left ( z-x \right )\left ( y-x \right )$
2. $\left ( x-z \right )\left ( y-z \right )$
3. $\left ( y-z \right )\left ( z-y \right )$
4. $\left ( y-z \right )\left ( x-z \right )$

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